Finite Group Databasebeta

← D61×#2239 #29834900

Subgroups — D61×#2239 #29834900

Order 15616.

552 conjugacy classes of subgroups.

The subgroup lattice has 440 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#470×D61C211yesmaximal, characteristic
2#430×D61C211yesmaximal, characteristic
3#21448040C212yesmaximal, complemented
4#21448039C211yesmaximal, characteristic, complemented
5#21448038C211yesmaximal, characteristic, complemented
6#21448037C212yesmaximal, complemented
7#21448036C211yesmaximal, characteristic, complemented
8#365×D61C212yesmaximal, complemented
9#362×D61C212yesmaximal, complemented
10#349×D61C211yesmaximal, characteristic
11C61×#2239C211yesmaximal, characteristic, complemented
12C2×Q16×D61C2211yescharacteristic
13C2×M16×D61—21no—
14C2×M16×D61C2211yescharacteristic
15C22⋊Q8×D61—21no—
16M32×D61C2212yes—
17#16840021C2211yescharacteristic
18#16840020C2211yescharacteristic
19#16840019—21no—
20#16840018—21no—
21#16840017C2211yescharacteristic
22#16839811C2211yescharacteristic
23#16839810—21no—
24#16839809—21no—
25#16839809C2212yes—
26#108×D61—21no—
27#108×D61C2212yes—
28#106×D61C2211yescharacteristic
29#103×D61—21no—
30#16839586C2212yescomplemented
31#16839585C2212yescomplemented
32#16839584C2212yescomplemented
33#16839579C2212yescomplemented
34#16839578C2212yescomplemented
35#16839577C2212yescomplemented
36#16839544C2211yescharacteristic
37#16839543C2212yes—
38C61×#470C2211yescharacteristic
39C61×#430C2211yescharacteristic
40C61×#365C2212yescomplemented
41C61×#362C2212yescomplemented
42C61×#349C2211yescharacteristic
43C2×Q8×D61—21no—
44C22×C4×D61D411yescharacteristic
45C2×Dic244C2311yescharacteristic
46C2×#11758202—21no—
47Q16×D61—22no—
48Q16×D61—22no—
49C2×#11758194—21no—
50C2×#11758194D411yescharacteristic
51C2×#11758189—41no—
52C2×#11758189D411yescharacteristic
53C2×#11758189C2311yescharacteristic
54M16×D61—22no—
55M16×D61—22no—
56M16×D61—22no—
57M16×D61—22no—
58M16×D61—41no—
59M16×D61—41no—
60C2×C8×D61—41no—
61C2×C8×D61D411yescharacteristic
62C2×C8×D61C2311yescharacteristic
63#14519757—21no—
64#14519756—21no—
65#14519755—41no—
66#14519754—41no—
67#14519753—21no—
68C4⋊C4×D61—21no—
69C4⋊C4×D61—41no—
70C22⋊C4×D61—41no—
71#14519717C2312yes—
72#14519716—22no—
73C16×D61—22no—
74#14519713—21no—
75#14519713C2312yes—
76#14519712—22no—
77#14519712—22no—
78#14519709C2311yescharacteristic
79#14519708—21no—
80#14519702—21no—
81#14519701—21no—
82#14519700—21no—
83C2×Q16×C61C2311yescharacteristic
84C2×M16×C61—21no—
85C2×M16×C61C2311yescharacteristic
86C22⋊Q8×C61—21no—
87M32×C61C2312yes—
88#108×C61—21no—
89#108×C61C2312yes—
90#106×C61C2311yescharacteristic
91#103×C61—21no—
92C23×D61SD1611yescharacteristic
93C2×Q8×C61—21no—
94C22×C4×C61C2×D411yescharacteristic
95C22×Dic61SD1611yescharacteristic
96Q8×D61—41no—
97Q8×D61—41no—
98Q8×D61—41no—
99Q8×D61—41no—
100C2×C4×D61—21no—
101C2×C4×D61—21no—
102C2×C4×D61—21no—
103C2×C4×D61—21no—
104C2×C4×D61—41no—
105C2×C4×D61—41no—
106C2×C4×D61SD1611yescharacteristic
107C2×C4×D61SD1611yescharacteristic
108C2×C4×D61C2×D411yescharacteristic
109C2×C4×D61C2×D411yescharacteristic
110C2×Dic122—21no—
111C2×Dic122—41no—
112Q16×C61—22no—
113M16×C61—22no—
114M16×C61—22no—
115M16×C61—41no—
116C2×C8×C61—41no—
117C2×C8×C61C2×D411yescharacteristic
118C2×C8×C61C2411yescharacteristic
119C4⋊C4×C61—21no—
120C4⋊C4×C61—41no—
121C22⋊C4×C61—41no—
122C22⋊Dic61—41no—
123#11758202—42no—
124#11758198—41no—
125#11758198—41no—
126C4⋊Dic61—21no—
127C4⋊Dic61—41no—
128#11758196—41no—
129#11758196—41no—
130#11758196—41no—
131#11758194—22no—
132#11758194—22no—
133#11758194—41no—
134C2×#92418—41no—
135C2×#92418C2×D411yescharacteristic
136C2×#92418C2×D411yescharacteristic
137Dic244—22no—
138#11758189—22no—
139#11758189—22no—
140#11758189—42no—
141#11758189—42no—
142C8×D61—21no—
143C8×D61—21no—
144C8×D61—42no—
145C8×D61—42no—
146C8×D61#4112yes—
147C8×D61#4112yes—
148C16×C61—22no—
149#11758185—22no—
150C23×C61C2×SD1611yescharacteristic
151C22×D61—21no—
152C22×D61—21no—
153C22×D61—42no—
154C22×D61C2×SD1611yescharacteristic
155C22×D61C2×SD1611yescharacteristic
156Q8×C61—41no—
157Q8×C61—41no—
158C2×C4×C61—21no—
159C2×C4×C61—21no—
160C2×C4×C61—41no—
161C2×C4×C61—41no—
162C2×C4×C61C2×SD1611yescharacteristic
163C2×C4×C61C22×D411yescharacteristic
164C2×Dic61—21no—
165C2×Dic61—21no—
166C2×Dic61—41no—
167C2×Dic61—41no—
168C2×Dic61C2×SD1611yescharacteristic
169C2×Dic61C2×SD1611yescharacteristic
170C4×D61—21no—
171C4×D61—21no—
172C4×D61—21no—
173C4×D61—21no—
174C4×D61—21no—
175C4×D61—21no—
176C4×D61—82no—
177C4×D61—81no—
178C4×D61—81no—
179C4×D61#12311yescharacteristic
180C4×D61#12311yescharacteristic
181C4×D61AGL(1,ℤ/8)11yescharacteristic
182C4×D61AGL(1,ℤ/8)11yescharacteristic
183Dic122—41no—
184Dic122—41no—
185Dic122—81no—
186Dic122—81no—
187C8×C61—21no—
188C8×C61—42no—
189C8×C61C2×#4112yes—
190#92418—21no—
191#92418—42no—
192#92418#12312yes—
193C2×#2239—611nomaximal, Sylow
194C22×C61—21no—
195C22×C61—41no—
196C22×C61C22×SD1611yescharacteristic
197C2×D61—22no—
198C2×D61—21no—
199C2×D61—42no—
200C2×D61—41no—
201C2×D61—81no—
202C2×D61#48111yescharacteristic
203C2×D61#48111yescharacteristic
204C4×C61—21no—
205C4×C61—81no—
206C4×C61—81no—
207C4×C61C2×#12311yescharacteristic
208C4×C61C2×AGL(1,ℤ/8)11yescharacteristic
209Dic61—21no—
210Dic61—81no—
211Dic61—81no—
212Dic61#48111yescharacteristic
213Dic61#48111yescharacteristic
214C2×#470—611no—
215C2×#430—611no—
216#2239—611no—
217#2239—611no—
218#2239—612no—
219#2239—612no—
220#2239—611no—
221#2239D6111yescharacteristic, direct product factor
222C2×#365—612no—
223C2×#362—612no—
224C2×#349—611no—
225C2×C61—21no—
226C2×C61—41no—
227C2×C61C2×#48111yescharacteristic
228D61—21no—
229D61—41no—
230D61#223912yesdirect product factor
231C22×Q16—611no—
232C22×M16—611no—
233C22×M16—1221no—
234C2×C22⋊Q8—1221no—
235C2×M32—612no—
236#470—611no—
237#470—611no—
238#470—611no—
239#470—1221no—
240#470—1221no—
241#470C2×D6111yescharacteristic
242#430—611no—
243#430—612no—
244#430—1221no—
245#430—1221no—
246#430C2×D6111yescharacteristic
247C2×#108—612no—
248C2×#108—1221no—
249C2×#106—611no—
250C2×#103—1221no—
251#365—612no—
252#365—612no—
253#365—612no—
254#365C2×D6112yescomplemented
255#362—612no—
256#362—612no—
257#362—612no—
258#362C2×D6112yescomplemented
259#349—611no—
260#349—612no—
261#349C2×D6111yescharacteristic
262C61C2×#223911yescharacteristic, complemented, Sylow
263C22×Q8—1221no—
264C23×C4—611no—
265C2×Q16—611no—
266C2×Q16—1222no—
267C2×Q16—1222no—
268C2×Q16—1221no—
269C2×Q16C22×D6111yescharacteristic
270C2×M16—21no—
271C2×M16—611no—
272C2×M16—611no—
273C2×M16—611no—
274C2×M16—1222no—
275C2×M16—1222no—
276C2×M16—1222no—
277C2×M16—1222no—
278C2×M16—1221no—
279C2×M16—2441no—
280C2×M16—2441no—
281C2×M16—2441no—
282C2×M16C22×D6111yescharacteristic
283C22×C8—611no—
284C22×C8—611no—
285C22×C8—2441no—
286C22⋊Q8—21no—
287C22⋊Q8—1221no—
288C22⋊Q8—1221no—
289C22⋊Q8—1221no—
290C22⋊Q8—2441no—
291C22⋊Q8—2441no—
292C2×C4⋊C4—1221no—
293C2×C4⋊C4—2441no—
294C2×C22⋊C4—2441no—
295M32—612no—
296M32—1222no—
297M32C22×D6112yes—
298C2×C16—1222no—
299#108—21no—
300#108—612no—
301#108—1222no—
302#108—1222no—
303#108—1221no—
304#108C22×D6112yes—
305#106—611no—
306#106—1221no—
307#106C22×D6111yescharacteristic
308#103—21no—
309#103—1221no—
310#103—1221no—
311#103—1221no—
312C24—611no—
313C2×Q8—21no—
314C2×Q8—1221no—
315C2×Q8—2441no—
316C2×Q8—2441no—
317C2×Q8—2441no—
318C2×Q8—2441no—
319C2×Q8—2441no—
320C22×C4—611no—
321C22×C4—611no—
322C22×C4—611no—
323C22×C4—611no—
324C22×C4—611no—
325C22×C4—1221no—
326C22×C4—1221no—
327C22×C4—1221no—
328C22×C4—1221no—
329C22×C4—2441no—
330C22×C4—2441no—
331C22×C4D4×D6111yescharacteristic
332Q16—22no—
333Q16—1222no—
334Q16—2442no—
335M16—22no—
336M16—22no—
337M16—41no—
338M16—1222no—
339M16—1222no—
340M16—1222no—
341M16—1222no—
342M16—2442no—
343M16—2442no—
344M16—2441no—
345C2×C8—41no—
346C2×C8—611no—
347C2×C8—612no—
348C2×C8—612no—
349C2×C8—611no—
350C2×C8—1221no—
351C2×C8—1221no—
352C2×C8—2442no—
353C2×C8—2442no—
354C2×C8—2441no—
355C2×C8D4×D6111yescharacteristic
356C2×C8C23×D6111yescharacteristic
357C4⋊C4—21no—
358C4⋊C4—41no—
359C4⋊C4—1221no—
360C4⋊C4—2441no—
361C4⋊C4—2441no—
362C4⋊C4—2441no—
363C4⋊C4—2441no—
364C22⋊C4—41no—
365C22⋊C4—2441no—
366C22⋊C4—2441no—
367C22⋊C4—2441no—
368C16—22no—
369C16—1222no—
370C23—611no—
371C23—611no—
372C23—1221no—
373C23—1221no—
374C23—2442no—
375C23SD16×D6111yescharacteristic
376Q8—41no—
377Q8—41no—
378Q8—4881no—
379Q8—4881no—
380Q8—2441no—
381Q8—2441no—
382C2×C4—21no—
383C2×C4—21no—
384C2×C4—41no—
385C2×C4—41no—
386C2×C4—611no—
387C2×C4—611no—
388C2×C4—611no—
389C2×C4—611no—
390C2×C4—611no—
391C2×C4—611no—
392C2×C4—1221no—
393C2×C4—1221no—
394C2×C4—1221no—
395C2×C4—1221no—
396C2×C4—1221no—
397C2×C4—1221no—
398C2×C4—1221no—
399C2×C4—1221no—
400C2×C4—4881no—
401C2×C4—4881no—
402C2×C4—4882no—
403C2×C4—2441no—
404C2×C4—2441no—
405C2×C4SD16×D6111yescharacteristic
406C2×C4C2×D4×D6111yescharacteristic
407C8—21no—
408C8—42no—
409C8—612no—
410C8—1221no—
411C8—2442no—
412C8#41×D6112yes—
413C22—21no—
414C22—41no—
415C22—611no—
416C22—611no—
417C22—1222no—
418C22—1221no—
419C22—4881no—
420C22—2441no—
421C22—2442no—
422C22C2×SD16×D6111yescharacteristic
423C4—21no—
424C4—81no—
425C4—81no—
426C4—611no—
427C4—611no—
428C4—1221no—
429C4—4881no—
430C4—4881no—
431C4#123×D6111yescharacteristic
432C4AGL(1,ℤ/8)×D6111yescharacteristic
433C2—21no—
434C2—41no—
435C2—612no—
436C2—1221no—
437C2—2441no—
438C2#481×D6111yescharacteristic
subgroupG/H
centerC2#481×D61
commutator, cosocleC2×C8×C61C24
FrattiniC2×C8C23×D61
FittingC61×#2239C2
socleC2×C61C2×#481
prime radicalC23×D61SD16
hypercenter#2239D61
hypocenterC61C2×#2239
LCSG ▷ C2×C8×C61 ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×M16 ◁ #2239

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
3. #21448040C2semidirect
4. #21448039C2semidirect
5. #21448038C2semidirect
6. #21448037C2semidirect
7. #21448036C2semidirect
8. #365×D61C2semidirect
9. #362×D61C2semidirect
11. C61×#2239C2semidirect
30. #16839586C22semidirect
31. #16839585C22semidirect
32. #16839584C22semidirect
33. #16839579C22semidirect
34. #16839578C22semidirect
35. #16839577C22semidirect
40. C61×#365C22semidirect
41. C61×#362C22semidirect
221. #2239D61direct (N × H)
230. D61#2239direct (N × H)
254. #365C2×D61semidirect
258. #362C2×D61semidirect
262. C61C2×#2239semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#470×D612
#430×D612
#214480402
#214480392
#214480382
#214480372
#214480362
#365×D612
#362×D612
#349×D612
C61×#22392
C2×#223961